## WG 1: Bounds on the Size of Network Codes

**Chairs:** Tuvi Etzion, Joachim Rosenthal

### Work programme

Traditional algebraic coding theory is aware of a number of existence bounds for linear and non-linear error-correcting codes. Among the restrictive examples of bounds, one has to mention the Plotkin and Elias-Bassalygo bound, the sphere-packing bound, the Singleton bound, whereas bounds like the Gilbert-Varshamov bound and the BCH-bound are assertive and often provide construction mechanisms for good codes. This Working Group will focus on the mathematical task to formulate and prove amended versions of traditional bounds, or to provide new bounds for network codes. From possible assertive bounds it is expected that new construction methods will be provided to the benefit of the work in Working Group 4.

**Survey with open problems**

- T. Etzion.
*Problems on q-Analogs in Coding Theory.*arXiv

### Member list

Current participants list of Working Group 1 with research interests

Paulo Almeida |
Department of Mathematics University of Aveiro, Portugal |

Convolutional codes, finite fields, superregular matrices, subspace codes | |

Christine Bachoc |
Bordeaux Institute of Mathematics University of Bordeaux, France |

Bounds and Constructions of Network Codes | |

Roland D. Barrolleta |
Information and Communications Engineering Autonomous University of Barcelona, Spain |

Information Theory, Coding Theory, Design Theory | |

Daniele Bartoli |
Department of Mathematics Ghent University, Belgium |

Coding Theory, Algebraic Codes, Functional Codes | |

Simon Blackburn |
Mathematics Department Royal Holloway, University of London, UK |

Combinatorics, Coding Theory, Cryptography | |

Sarit Buzaglo |
Computer Science Department (–14) Technion, Israel |

Algebraic Coding Theory, Error-Correcting Codes for Non-Volatile Memories, Discrete Geometry and Combinatorics | |

Eimear Byrne |
School of Mathematics and Statistics University College Dublin, Ireland |

Codes over Rings, Decoding Algorithms, Network Coding, Codes and Combinatorial Structures | |

Ilaria Cardinali |
Department of Information Engineering and Mathematics University of Siena, Italy |

Polar Grassmannians, Grassmann Codes, Projective Linear Codes | |

Joan-Josep Climent |
Department of Statistics and Operations Research University of Alicante, Spain |

Linear Algebra, Coding Theory, Cryptography | |

Jan De Beule |
Department of Mathematics Free University of Brussels, Belgium |

Finite Geometry, Coding Theory | |

Sara Díaz Cardell |
Department of Statistics and Operations Research (–15) University of Alicante, Spain |

Coding Theory, Cryptology, Computational Security, Network Coding | |

Doris Dumičić Danilović |
Department of Mathematics University of Rijeka, Croatia |

Design Theory, Coding Theory | |

Andreas-Stephan Elsenhans |
Institute of Mathematics University of Paderborn, Germany |

| |

Tuvi Etzion |
Computer Science Department Technion, Israel |

Coding Theory, Digital Sequences, Block Design | |

Szabolcs Levente Fancsali |
Institute of Mathematics Eötvös Loránd University, Hungary |

Finite geometry (t-spreads); Network coding and secret sharing | |

Thomas Feulner |
Institute for Mathematics (–13) University of Bayreuth, Germany |

Automorphism Group, Equivalence, Bounds, Construction | |

Ragnar Freij |
Institute for Communications Engineering Technical University of Munich, Germany |

Matroid theory in networks, Algebraic graph theory and relations to consensus algorithms | |

Luca Giuzzi |
DICATAM - Section of Mathematics University of Brescia, Italy |

Coding theory; Cryptography; Finite Geometry | |

Marcus Greferath |
Department of Mathematics and Systems Analysis Aalto University, Finland |

Algebraic Coding Theory, q-ary Designs; Fourier inversion, MÃ¶bius inversion, Exponential sums | |

Edmundo J. Huertas Cejudo |
Department of Mathematics University of Coimbra, Portugal |

Network coding for throughput and reliability improvement. Bounds and construction of network codes. | |

José Ignacio Iglesias Curto |
Department of Mathematics University of Salamanca, Spain |

Convolutional codes, algebraic geometric codes, decoding algorithms, optimal constructions | |

Petteri Kaski |
Department of Information and Computer Science Aalto University, Finland |

| |

Michael Kiermaier |
Institute for Mathematics University of Bayreuth, Germany |

Codes over Rings, Finite Geometry, Computer-aided Construction of Combinatorial Objects | |

†Axel Kohnert |
Institute for Mathematics University of Bayreuth, Germany |

Construction, Classification, Bounds, Foundations | |

Vedran Krcadinac |
Department of Mathematics, Faculty of Science University of Zagreb, Croatia |

q-Analogs of Designs | |

Sascha Kurz |
Institute for Mathematics University of Bayreuth, Germany |

Random Network Coding, Exhaustive Search, Integer Linear Programming | |

Ivan Landjev |
Department of Informatics New Bulgarian University, Bulgaria |

Network Codes, q-Analogs of Designs, Chain Ring Analogs of Designs, Bounds for Network Codes | |

José María Muñoz Porras |
Department of Mathematics University of Salamanca, Spain |

Convolutional codes, algebraic geometric codes, decoding algorithms, optimal constructions | |

Anamari Nakic |
Faculty of Electrical Engineering and Computing University of Zagreb, Croatia |

Designs over GF(q) | |

Patric Östergård |
Dpt. of Communications and Networking Aalto University, Finland |

Coding Theory, Combinatorial Algorithms, Design Theory | |

Ferruh Özbudak |
Institute of Applied Mathematics Middle East Technical University, Turkey |

| |

Francesco Pavese |
Dpt. of Mathematics, Informatics and Economics University of Basilicata, Italy |

Construction of Network Codes and Grassmannian Codes, Bounds on the Size of Network Codes | |

Ruud Pellikaan |
Discrete Mathematics Technical University Eindhoven, Netherlands |

Error Correcting Codes, Algebraic Geometry Codes, Code Based Cryptography | |

Raquel Pinto |
Department of Mathematics University of Aveiro, Portugal |

Bounds on the Size of Network Codes and Construction of Network Codes and Grassmannian Codes | |

Alberto Ravagnani |
Institute of Mathematics University of Neuchâtel, Switzerland |

Network Coding | |

Netanel Raviv |
Computer Science Department Technion, Israel |

Network Coding, Subspace Codes, Designs over Finite Fields | |

Josep Rifà |
Information and Communications Engineering Autonomous University of Barcelona, Spain |

Combinatorics, Coding Theory, Cryptography | |

Joachim Rosenthal |
Institute of Mathematics University of Zurich, Switzerland |

Network Codes, Schubert Calculus, Convolutional Codes | |

Maria Conceição Santos Rocha |
Department of Mathematics University of Aveiro, Portugal |

Network coding, error-correcting codes | |

Natalia Silberstein |
Computer Science Department Technion, Israel |

Coding for distributed storage systems, coding in projective spaces | |

Rita Simões |
Department of Mathematics University of Aveiro, Portugal |

| |

Xaro Soler |
Department of Statistics and Operations Research University of Alicante, Spain |

Finite Group Theory, Network Coding | |

Leo Storme |
Department of Mathematics Ghent University, Belgium |

Coding Theory Related to Finite Geometry, Designs | |

Emilio Suarez-Canedo |
Information and Communications Engineering Autonomous University of Barcelona, Spain |

Information Theory, Coding Theory, Design Theory | |

Andrea Svob |
Department of Mathematics University of Rijeka, Croatia |

Design Theory, Coding Theory | |

Marisa Toste |
School of Technology and Management Polytechnic Institute of Coimbra, Portugal |

| |

Paolo Vettori |
Department of Mathematics University of Aveiro, Portugal |

Construction of Network Codes and Convolutional Network Codes | |

Mercè Villanueva |
Information and Communications Engineering Autonomous University of Barcelona, Spain |

Information Theory, Coding Theory, Distributed Storage | |

Antonia Wachter-Zeh |
Institute for Communications Engineering Technical University of Munich, Germany |

Network coding, Rank metric codes (Gabidulin codes) | |

Alfred Wassermann |
Institute for Mathematics University of Bayreuth, Germany |

Construction of Network Codes, Isomorphisms | |

Thomas Westerbäck |
Department of Mathematics KTH Royal Institute of Technology, Sweden |

Codes over Rings, Combinatorics | |

Alexander Zeh |
Computer Science Department (–16) Technion, Israel |

Reed-Solmon Codes, Cyclic Codes, List Decoding |